This shoot is definitely growing bigger and greener

The Labor Department reported today that seasonally adjusted new claims for unemployment insurance fell by 34,000 to 601,000 for the most recent available week, resulting in a reduction of the 4-week average for this series for the fourth consecutive week in a row.

We have been highlighting these numbers for the last four weeks ([1], [2], [3], [4]), inspired by a brief statement that appeared in the Wall Street Journal on March 28. The WSJ reported that Robert Gordon, professor of economics at Northwestern University and highly regarded business cycle expert, had noticed that the 4-week average of new unemployment claims tended to peak shortly before the end of historical recessions. I was pleased to see that last week Gordon weighed in in person with his view of these data.

The key question of course is whether the recent declines in new claims mean that we’re really past the peak for this business cycle, or whether we could see more bad news in the weeks ahead that bring these numbers up to new highs. In my April 23 and April 30 analyses, I proposed a way to think about this question nonparametrically, that is, without making any statistical assumptions other than that the future will be like the past, simply by counting the number of weeks in previous recessions that were as favorable as we’d seen up to that point but proved to be a false positive signal. Those calculations led me to conclude that the odds were 2 to 1 that the data as of April 23 would later come to be seen as a false positive, but roughly even once we received the more favorable data of April 30.

In his May 1 write-up, Gordon performed a similar calculation to mine, though whereas I used weeks as the basic unit of observation (counting 11 out of 22 false positives), Gordon categorized the data in terms of “episodes” (with 4 out of 8 false positives). In the absence of a clear a priori definition of an “episode”, I prefer my metric, but it is interesting and reassuring that we both arrived at the same basic conclusion. Gordon went on to investigate a number of other features of a downturn, such as the length that the recession had already proceeded and the sharpness of the increases prior to the candidate peak. But it is always tricky to rely on those sorts of refinements when one is trying to draw an inference from the limited number of observations that we have available.

I’d pushed the nonparametric approach more or less as far as I was comfortable with last week, and if we want to say something useful about the way that the latest data have strengthened the signal we really need to use more parametric tools that capture some of the key dynamic properties of the new claims numbers themselves. For this purpose, I built a very simple model to forecast the seasonally adjusted new claims number (yt) in terms of its value the previous week (yt-1), the 4-week average the previous week (xt-1), and whether or not we’re currently in a recession, with st=1 if NBER says week t is part of a recession, and st=0 if expansion:

This relation was estimated by ordinary least squares, with standard errors in parentheses. The model implies a great deal of persistence in the new claims numbers, though given enough time the process would revert to historical mean values. If we were certain that the current recession is going to last forever, the forecast from here would go back up and eventually stabilize at a value of 650,000 new claims each week, 27,000 higher than the most recent average.

Imposing the certainty that the recession is going to last forever, however, hardly seems the correct approach. I’ve instead adopted the perspective that there’s a 1.56% chance of it ending in any given week, based on the observation that in the 384 recession weeks between 1969 and 2009, we saw 6 recoveries (6/384 = 0.0156). If you use that assumption from here out (i.e., that st obeys a time-homogenous Markov chain), you’d be predicting that, in the absence of any other indications to the contrary, there’s a 6% chance that we’ll be out of recession in 4 weeks, a 22% chance we’ll be out in 16 weeks, and a 50% chance we’ll be out in 48 weeks. Those seem to me like pretty reasonable numbers to use.

I then calculated dynamic forecasts of the above model with these assumed transition probabilities for st+j. Aficionados will recognize this as a Markov-switching autoregression with directly observable regimes. The diagram below plots the actual weekly data up through this point in black, the 4-week averages in blue, and forecasts of the future 4-week averages from here out as the dashed blue line. Basically the unconditional likelihood that the recession will eventually end slightly outweighs the tendency of new claims to rise if we stay in a recession, and the forecast declines slowly from its current value.

The above graph also plots 70% confidence intervals calculated from this dynamic simulation. The model implies that there is a 15% chance of seeing the new claims numbers go back up above their peak of 4 weeks ago. In other words, there’s an 85% chance that the worst numbers for this particular series are now behind us.

Here is how Gordon summarized the numbers that we had available a week ago:

It is always too early to make definitive conclusions, but the recent 2009 peak in new claims looks sufficiently similar to previous recession peaks to allow a conclusion that it is highly probable that the new claims peak has now occurred. The evidence provided here suggests several differences between the recent peak and previous false peaks in earlier recessions. The recent peak occurred much later in the recession than previous false peaks, and the run-up of new claims in the two months prior to the recent peak was substantially faster than in previous false peaks….

My reasoning leads me to conclude that the ultimate NBER trough of the current business cycle is likely to occur in May or June 2009, substantially earlier than is currently predicted by many professional forecasters.

Today’s data make Gordon’s prediction look even better.

Originally published at Econbrowser and reproduced here with the author’s permission.